Problem: If $x$ satisfies $\frac{1}{2}-\frac{1}{3}=\frac{3}{x}$, then what is the value of $x$ ?
Solution: We have $\frac{3}{x} = \frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac26 =\frac16$.  Cross-multiplying $\frac3x =\frac16$ gives $x = \boxed{18}$.